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  4. A uniform sphere of weight w and radius 3 m is being held by a string of length 2 m and attached to a frictionless wall, as shown in the figure. The tension in the string will be <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-e3kbsxkmsaemenj7.jpg />

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Q. A uniform sphere of weight $w$ and radius $3 \, m$ is being held by a string of length $2 \, m$ and attached to a frictionless wall, as shown in the figure. The tension in the string will be
Question

NTA AbhyasNTA Abhyas 2022

Solution:

Solution
From geometry:
$cos \theta =\frac{3}{5}$
$sin \theta =\frac{4}{5}$
As the sphere is at equilibrium
$Tsin \theta =w$
$T=\frac{5 w}{4}$